Consider a test of H0 : μ ≤ 100 versus H1 : μ > 100. Suppose that a sample of size 20 has a sample mean of X = 105. Determine the p-value of this outcome if the population standard deviation is known to equal (a) 5; (b) 10; (c) 15.
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Consider a test of H0 : μ ≤ 100 versus H1 : μ > 100. Suppose that a sample of size 20 has a
sample mean of X = 105. Determine the p-value of this outcome if the population standard
deviation is known to equal
(a) 5; (b) 10; (c) 15.
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- In a test of H0: p = 0.8 against H1: p ≠ 0.8, a sample of size 1000 produces Z = 2.05 for the value of the test statistic. Thus the p-value (or observed level of significance) of the test is approximately equal to:Assume that you have a sample of n1=8, with the sample mean X1=44, and a sample standard deviation of S1=5, and you have an independent sample of n2=14 from another population with a sample mean of X2=30 and the sample standard deviation S2=6. Using a significance level of α=0.025, what is the critical value for a one-tail test of the hypothesis H0: μ1≤ μ2 against the alternative H1: μ1>μ2? The critical value is ______ (Round to two decimal places as needed.)Suppose X1, ..., Xn have been randomly sampled from a normal distribution with mean 0 and unknown variance sigma^2, and let U = c * i=1 -> n summation (X_ i)^2 , where c is a constant. Find the value of c that minimises the Mean Squared Error (MSE)
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- A random sample of size n = 4 taken from a normal population with σ2 = 9 is used to test H0 : µ = µ0against H1 : µ = µ1 where µ1 > µ0. e null hypothesis will be rejected if X > µ ¯0 + 2.5. Find the levelof significance of the critical regionWe want to use a z-test to determine if the sample mean is greater than 20 at the alpha = 0.05. What is the critical value(s)?